Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 51, pp. 1-21.

Title: Monotone iteration scheme and its application to partial differential equation 
       systems with mixed nonlocal and degenerate diffusions

Authors: Qiuling Huang (Shandong Univ. of Finance and Economics, Jinan, China)
         Xiaojie Hou (Univ. of North Carolina Wilmington, NC, USA)

Abstract:
 A monotone iteration scheme for traveling waves based on ordered upper
 and lower solutions is derived for a class of nonlocal dispersal system
 with delay. Such system can be used to study the competition among
 nonlocally diffusive species and degenerately diffusive species.
 An example of such system is studied in detail. We show the existence
 of the traveling wave solutions for this system by this iteration scheme.
 In addition, we study the minimal wave speed,  uniqueness, strict
 monotonicity and  asymptotic behavior of the traveling wave solutions. 

Submitted May 6, 2018. Published April 18, 2019.
Math Subject Classifications: 35C07, 35B40.
Key Words: Nonlocal diffusion; traveling wave solution; asymptotics;
          Schauder fixed point theorem; upper and lower solutions; uniqueness.